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Proof step 13 from proof validref-subspec-samesubclasses-01 (previous step)

ty .jtelemtype .class = `java.lang.Object' .class, same-subclasses-contains(`java.lang.Object' .class, str, str0), junkref(str, r, st), has_classtype(st[r -- _type] .type), ty .jtdims < st[r -- _type] .type .jtdims, has_classtype(ty), is_valid_ref(str0, r, st) ⊦ r = jvmref, tdname+∃(str0, st[r -- _type] .type .jtelemtype .class), junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), st[r -- _type] .type .jtelemtype .class ≤ `java.lang.Object' .class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬ type∃(str, st[r -- _type] .type) ∧ r ≠ jvmref → ¬ is_valid_ref(str, r, st)
Proof step 12:
¬ (¬ type∃(str0, st[r -- _type] .type) ∧ r ≠ jvmref), ty .jtelemtype .class = `java.lang.Object' .class, same-subclasses-contains(`java.lang.Object' .class, str, str0), junkref(str, r, st), has_classtype(st[r -- _type] .type), ty .jtdims < st[r -- _type] .type .jtdims, has_classtype(ty), is_valid_ref(str0, r, st) ⊦ r = jvmref, tdname+∃(str0, st[r -- _type] .type .jtelemtype .class), junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), st[r -- _type] .type .jtelemtype .class ≤ `java.lang.Object' .class

Rule argument

[speclemmaarg: , ¬ type∃(str, st[r -- _type] .type) ∧ r ≠ jvmref → ¬ is_valid_ref(str, r, st) ,[st, r, str] → [st, r, str0] ,F ,addfuns , ,is_valid_ref-typeex ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str0)]]